<TeXmacs|1.99.18>

<style|<tuple|tmdoc|maxima|english|old-spacing|old-dots|old-lengths>>

<\body>
  <\tmdoc-title>
    Example <name|Octave> session
  </tmdoc-title>

  An <name|Octave> session is started using <menu|Insert|Session|Octave>.
  Below, it is shown how to do linear algebra operations with <name|Octave>,
  such as matrix multiplication, inversion and diagonalization.

  <\session|octave|default>
    <\output>
      GNU Octave (5.2.0) Session in GNU TeXmacs

      Welcome to star and fork it at https://github.com/texmacs/octave
    </output>

    <\input>
      \<gtr\>\<gtr\>\ 
    <|input>
      A=[1 0 0 0;2 2 0 0;-1 0 2 0;0 -1 2 2]
    </input>

    <\unfolded-io>
      \<gtr\>\<gtr\>\ 
    <|unfolded-io>
      A
    <|unfolded-io>
      <with|mode|math|math-display|true|<matrix|<tformat|<table|<row|<cell|<with|mode|math|1>>|<cell|<with|mode|math|0.0>>|<cell|<with|mode|math|0.0>>|<cell|<with|mode|math|0.0>>>|<row|<cell|<with|mode|math|2>>|<cell|<with|mode|math|2>>|<cell|<with|mode|math|0.0>>|<cell|<with|mode|math|0.0>>>|<row|<cell|<with|mode|math|-1>>|<cell|<with|mode|math|0.0>>|<cell|<with|mode|math|2>>|<cell|<with|mode|math|0.0>>>|<row|<cell|<with|mode|math|0.0>>|<cell|<with|mode|math|-1>>|<cell|<with|mode|math|2>>|<cell|<with|mode|math|2>>>>>>>
    </unfolded-io>

    <\unfolded-io>
      \<gtr\>\<gtr\>\ 
    <|unfolded-io>
      A^2
    <|unfolded-io>
      <with|mode|math|math-display|true|<matrix|<tformat|<table|<row|<cell|<with|mode|math|1>>|<cell|<with|mode|math|0.0>>|<cell|<with|mode|math|0.0>>|<cell|<with|mode|math|0.0>>>|<row|<cell|<with|mode|math|6>>|<cell|<with|mode|math|4>>|<cell|<with|mode|math|0.0>>|<cell|<with|mode|math|0.0>>>|<row|<cell|<with|mode|math|-3>>|<cell|<with|mode|math|0.0>>|<cell|<with|mode|math|4>>|<cell|<with|mode|math|0.0>>>|<row|<cell|<with|mode|math|-4>>|<cell|<with|mode|math|-4>>|<cell|<with|mode|math|8>>|<cell|<with|mode|math|4>>>>>>>
    </unfolded-io>

    <\unfolded-io>
      \<gtr\>\<gtr\>\ 
    <|unfolded-io>
      tmdisp(A.^2)
    <|unfolded-io>
      <with|mode|math|math-display|true|<matrix|<tformat|<table|<row|<cell|<with|mode|math|1>>|<cell|<with|mode|math|0.0>>|<cell|<with|mode|math|0.0>>|<cell|<with|mode|math|0.0>>>|<row|<cell|<with|mode|math|4>>|<cell|<with|mode|math|4>>|<cell|<with|mode|math|0.0>>|<cell|<with|mode|math|0.0>>>|<row|<cell|<with|mode|math|1>>|<cell|<with|mode|math|0.0>>|<cell|<with|mode|math|4>>|<cell|<with|mode|math|0.0>>>|<row|<cell|<with|mode|math|0.0>>|<cell|<with|mode|math|1>>|<cell|<with|mode|math|4>>|<cell|<with|mode|math|4>>>>>>>
    </unfolded-io>

    <\input>
      \<gtr\>\<gtr\>\ 
    <|input>
      [u,v]=eig(A)
    </input>

    <\input>
      \<gtr\>\<gtr\>\ 
    <|input>
      Q=[1 0 0 0;-2 2 1 0;1 1 0 0;-4 0 0 -1]
    </input>

    <\input>
      \<gtr\>\<gtr\>\ 
    <|input>
      P=inv(Q)
    </input>

    <\unfolded-io>
      \<gtr\>\<gtr\>\ 
    <|unfolded-io>
      P*A*Q
    <|unfolded-io>
      <with|mode|math|math-display|true|<matrix|<tformat|<table|<row|<cell|<with|mode|math|1>>|<cell|<with|mode|math|0.0>>|<cell|<with|mode|math|0.0>>|<cell|<with|mode|math|0.0>>>|<row|<cell|<with|mode|math|0.0>>|<cell|<with|mode|math|2>>|<cell|<with|mode|math|0.0>>|<cell|<with|mode|math|0.0>>>|<row|<cell|<with|mode|math|0.0>>|<cell|<with|mode|math|0.0>>|<cell|<with|mode|math|2>>|<cell|<with|mode|math|0.0>>>|<row|<cell|<with|mode|math|0.0>>|<cell|<with|mode|math|0.0>>|<cell|<with|mode|math|1>>|<cell|<with|mode|math|2>>>>>>>
    </unfolded-io>

    <\input>
      \<gtr\>\<gtr\>\ 
    <|input>
      \;
    </input>
  </session>

  The second part shows the graph capacity of Octave, 2D and 3D graphs.

  <\session|octave|default>
    <\input>
      \<gtr\>\<gtr\>\ 
    <|input>
      x=linspace(-10,10,1000);
    </input>

    <\input>
      \<gtr\>\<gtr\>\ 
    <|input>
      y=x+sin(x);
    </input>

    <\unfolded-io>
      \<gtr\>\<gtr\>\ 
    <|unfolded-io>
      plot(x,y,";Function y=x+sin(x);")
    <|unfolded-io>
      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20736574646173680A302E313520302E313520302E313520430A3131323320363831204D0A30203532353920560A7374726F6B650A5B5D203020736574646173680A302E313520302E313520302E313520430A3737363220363831204D0A30203532353920560A7374726F6B650A312E30303020554C0A4C54620A302E303020302E303020302E303020430A67726573746F7265202520636F6C6F75722070616C6574746520656E640A7374726F6B650A67726573746F72650A656E640A73686F77706167650A2525547261696C65720A2525446F63756D656E74466F6E74733A2048656C7665746963610A>|ps>|0.618par|||>
    </unfolded-io>

    <\input>
      \<gtr\>\<gtr\>\ 
    <|input>
      \;
    </input>
  </session>

  <\session|octave|default>
    <\input>
      \<gtr\>\<gtr\>\ 
    <|input>
      tx = ty = linspace (-8, 8, 41)';
    </input>

    <\input>
      \<gtr\>\<gtr\>\ 
    <|input>
      [xx, yy] = meshgrid (tx, ty);
    </input>

    <\input>
      \<gtr\>\<gtr\>\ 
    <|input>
      r = sqrt (xx .^ 2 + yy .^ 2) + eps;
    </input>

    <\input>
      \<gtr\>\<gtr\>\ 
    <|input>
      tz = sin (r) ./ r;
    </input>

    <\input>
      \<gtr\>\<gtr\>\ 
    <|input>
      mesh (tx, ty, tz);
    </input>

    <\input>
      \<gtr\>\<gtr\>\ 
    <|input>
      xlabel ("tx");
    </input>

    <\input>
      \<gtr\>\<gtr\>\ 
    <|input>
      ylabel ("ty");
    </input>

    <\input>
      \<gtr\>\<gtr\>\ 
    <|input>
      zlabel ("tz");
    </input>

    <\unfolded-io>
      \<gtr\>\<gtr\>\ 
    <|unfolded-io>
      title ("3-D Sombrero plot")
    <|unfolded-io>
      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    </unfolded-io>

    <\input>
      \<gtr\>\<gtr\>\ 
    <|input>
      \;
    </input>
  </session>

  <tmdoc-copyright|2003\U2021|Chu-Ching Huang|Joris van der Hoeven|Darcy
  Shen>

  <tmdoc-license|Permission is granted to copy, distribute and/or modify this
  document under the terms of the GNU Free Documentation License, Version 1.1
  or any later version published by the Free Software Foundation; with no
  Invariant Sections, with no Front-Cover Texts, and with no Back-Cover
  Texts. A copy of the license is included in the section entitled "GNU Free
  Documentation License".>
</body>

<initial|<\collection>
</collection>>